Valeria has a points card for a movie theater.
She receives 80 rewards points just for signing up.
She earns 7.5 points for each visit to the movie theater.
She needs 185 points for a free movie ticket.

Write and solve an equation which can be used to determine vv, the number of visits Valeria must make to earn a free movie ticket.

To determine the number of visits Valeria needs to make to earn a free movie ticket, let's break down the information:

- Valeria starts with 80 points.
- She earns 7.5 points for each visit.
- She needs 185 points to get a free movie ticket.

Let \( v \) represent the number of visits Valeria needs to make. The total points Valeria will have after \( v \) visits is the sum of her initial points and the points she earns from the visits. This can be modeled with the following equation:

\[
80 + 7.5v = 185
\]

### Solving for \( v \):

1. Subtract 80 from both sides:

\[
7.5v = 185 - 80
\]

\[
7.5v = 105
\]

2. Divide both sides by 7.5 to solve for \( v \):

\[
v = \frac{105}{7.5}
\]

\[
v = 14
\]

### Conclusion:
Valeria must make **14 visits** to earn a free movie ticket.

Would you like more details on the steps? Also, here are 5 related questions to practice:

1. If Valeria earns 10 points per visit instead of 7.5, how many visits would she need for a free ticket?
2. How many points will Valeria have after 20 visits?
3. If she needs 250 points for a special reward, how many visits would it take?
4. What would happen if Valeria only received 5 points per visit?
5. How many visits does she need if she starts with 100 points instead of 80?

**Tip:** When setting up equations for real-life situations, always define your variable and make sure the equation matches the problem's conditions.

Valeria has a points card for a movie theater. She receives 80 rewards points just for signing up. She earns 7.5 points for each visit to the movie theater. She needs 185 points for a free movie ticket. Write and solve an equation which can be used to determine v, the number of visits Valeria must make to earn a free movie ticket.

Discover how to solve a linear equation to find the number of visits Valeria must make to earn a free movie ticket. She starts with 80 points and earns 7.5 points per visit, needing 185 points total. This problem is perfect for Grades 6-8 students learning basic algebra and linear equations.

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